Answer:
[tex]\angle ABD =42.4^{\circ}[/tex]
Step-by-step explanation:
We are given that Point C is in the interior of ∠ABD
We are also given that ∠ABC ≅ ∠CBD
Now ,
[tex]\angle ABC = (\frac{5}{8}x + 18)\\\angle CBD = (4x)[/tex]
Since we are given that ∠ABC ≅ ∠CBD
So, [tex]\frac{5}{8}x + 18=4x\\4x-\frac{5}{8}x=18\\\frac{32x-5x}{8}=18\\\frac{27x}{8}=18\\x=\frac{18 \times 8}{27}\\x=5.3[/tex]
[tex]\angle CBD = (4x)=4(5.3)=21.2^{\circ}[/tex]
[tex]\angle ABD = \angle CBD+\angle ABC=21.2+21.2=42.4^{\circ}[/tex]
Hence [tex]\angle ABD =42.4^{\circ}[/tex]
